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Homework Help: An Osculating Circle HELPPP plZZ

  1. Nov 24, 2007 #1
    An Osculating Circle!! HELPPP plZZ urgent

    1. The problem statement, all variables and given/known data
    find the values of h,k and a that make the circle (x-h)^2+(y-k)^2=a^2 tangent to the parabola y=x^2+1 at the point (1,2) annd that also make the second derivatives d^2y/dx^2 have the same value on both courves.
     
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  3. Nov 25, 2007 #2

    HallsofIvy

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    Science Advisor

    What have YOU done? You need to find three values, h, k, and a, and you have three pieces of information: the circle passes through (1, 2):[itex](1-h)^2+ (2-k)^2= a^2[/itex]; The derivative of [itex](x-h)^2+ (y-k)^2= a^2[/itex] at (1, 2) is the same as the derivative of [itex]y= x^2+ 1[/itex] at (1, 2); the second derivative of [itex](x-h)^2+ (y-k)^2= a^2[/itex] at (1, 2) is the same as the second derivative of [itex]y= x^2+1[/itex] at (1, 2). The first and second derivatives of [itex]y= x^2+ 1[/itex] at (1,2) are easy. I would recommend using "implicit differentiation" to find the derivatives of [itex](x-h)^2+ (y-k)^2= a^2[/itex].
     
    Last edited by a moderator: Nov 25, 2007
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